I am referring to the algorithm that is used to give query suggestions when a user types a search term in Google.
I am mainly interested in: 1. Most important resul
Take a look at Firefox's Awesome bar algorithm
Google suggest is useful, because it take the millions of popular queries + your past related queries into account.
It doesn't have a good completion algorithm / UI though:
tomcat tut --> correctly suggest "tomcat tutorial". Now try tomcat rial --> no suggestions )-: